So far so good. Nice job! Yes, just multiply the -1/√3 by √3/√3 to move the radical to the numerator then you can subtract it from the 5√3.
1 √3
5√3 - ---- * ----
√3 √3
If you have more questions, just ask.
Philip P.
tutor
5√3 - √3/3 = (5 - 1/3)*√3 = (15/3 - 1/3)*√3 = (14/3)√3 or 14√3/3
Yes, you cannot simplify 3√2 - 2√3 because the radicals are different. Square roots are just numbers. If I have 5*6 - 3*6, I can factor out the common term (6): (5-3)*6 = 2*6. But if I have different numbers such as 5*6 - 4*7, I I have no common term I can factor out. Works the same with radicals, which are just numbers, and √2 is a different number than √3.
For a problem like √5+1)/(√5-1), you did the right thing by multiplying by the conjugate (√5+1)/(√5+1). The most simplified answer is the second one, (3+√5)/2
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08/07/14
John B.
So my thought that 5√3 - √3 = 4√3 is inaccurate. You cannot subtract the coefficient even if the radical is the same?
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08/07/14
John B.
Also, you have been so helpful-- how do I "rate" or give feedback for how good you were on this site?
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08/07/14
Philip P.
tutor
Hi John. It's not 5√3 - √3, it's 5√3 - (1/3)√3:
1 √3 √3 √3
--- * --- = ------- = ---- or (1/3)√3
√3 √3 (√3)2 3
Feedback is a "thumbs up" vote or "answered by". Glad to help
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08/07/14
John B.
3 is the answer?
√5 – 1
would get down to 6 + 2√5
4
or would I just simplify to 3 +√5
2
Thanks for your assistance.
08/07/14